Data-Driven Model Reduction and Transfer Operator Approximation
By Stefan Klus, Feliks Nuske, Péter Koltai, Hao Wu, Ioannis G. Kevrekidis, Christof Schutte, Frank No'e. Journal of nonlinear science, 2017
323 citations recorded by the source corpus.
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.
Subfields: Computational Mathematics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b54dfe1113dc9c17b279161f15d30909f4c785ca
How researchers see this paper
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In Computer Vision and Pattern Recognition
In Statistical and Nonlinear Physics
- Frank No'e
- Hao Wu
- Cecilia Clementi
- Sebastian Peitz
- Feliks Nuske
- Luca Pasquali
- Andreas Mardt
- Stefan Klus
Citations in the corpus
- Data-driven approximation of the Koopman generator: Model reduction, system identification, and control (2019, methodology): “Standard EDMD would typically need more test points for such an accurate approximation of the dominant eigenfunctions, see [35] for details.”
- VAMPnets for deep learning of molecular kinetics (2017, methodology): “For an introduction to the Koopman operator, please refer to [24, 30, 54].”
- Error bounds for kernel-based approximations of the Koopman operator (2023, methodology): “(b) The functions (cid:98) e j have unit length in the empirical L 2 µ -norm: Therefore, projecting onto the first N empirical Mercer features is the whitening transformation commonly used in traditional EDMD [24].”